Four years ago, the ratio of the ages of two friends P and Q was 4 : 5. Eight years hence, the ratio of their ages will be 11 : 13. What is the ratio of their present ages?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 9 : 11
Take the ages of four years ago as the unknowns; eight years hence is 12 years after that time.
Four years ago: P \(=4k\), Q \(=5k\)
\(\displaystyle \frac{4k+12}{5k+12}=\frac{11}{13}\)
\(13(4k+12)=11(5k+12)\), so \(52k+156=55k+132\) and \(k=8\)
P now \(=32+4=36\) years, Q now \(=40+4=44\) years
Ratio of present ages \(=36:44=9:11\)